We show that the partial compactification of a stratum of Abelian differentials previously considered by Mirzakhani and Wright is not an algebraic variety. Despite this, we use a combination of algebro‐geometric and other methods to provide a short, unconditional proof of Mirzakhani and Wright's formula for the tangent space to the boundary of a $G{L}^{+}(2,\mathbb{R})$ orbit closure, and give new results on the structure of the boundary.

中文翻译：

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所见即所得的压缩

我们表明，先前由Mirzakhani和Wright考虑的Abelian微分层的部分压实不是代数变体。尽管如此，我们还是结合使用了代数几何和其他方法，以提供一个简短的，无条件的Mirzakhani和Wright公式的正切空间与a的边界的切线的证明。$G{\mathrm{大号}}^{+}（\mathrm{2个}，\mathbb{[R}）$ 轨道闭合，并在边界结构上给出新结果。